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UBC Theses and Dissertations

Leveraging eigenvalue veering for improved sensing with microelectromechanical systems Reynen, Gregory Peter


Energy localization in nearly periodic microsystems can be leveraged to create a new sensing paradigm that is orders of magnitude more sensitive than current resonant-frequency based systems. In this thesis, the theory which supports this claim is independently developed from a mathematical description of a two degree-of-freedom resonant system. A novel proof-of-concept microelectromechanical system (MEMS) was also designed and fabricated to support the theoretical claims. The system employed a unique resonator design with two different approaches to inducing asymmetry in the system which in turn leads to the localization of energy in one of the resonators. The system proved the resonant frequency dependence on disorder in the system and also showed that the eigenvector sensitivity to disorder was at least an order of magnitude greater than the frequency sensitivity. However, the eigenvector sensitivity could not be matched with theory. This was likely due to the time-varying nature of the coupling spring stiffness (up to a 300% change in magnitude). The coupling spring stiffness was time-varying due to the inverse cubic relationship to coupling gap distance. The gap distance changes with time since it is practically impossible to excite only the common mode, leading to a superposition with the anti-phase mode. This was partially due to the input signal displaying non harmonic tendencies. At the same time, energy localization in the system leads to different amplitudes of vibration for each resonator which will also lead to gap distance modulation. A three degree-of-freedom system was also examined theoretically with different approaches to stiffness perturbation and the resultant sensitivity expressions which can be leveraged for improved sensors were developed. The analysis shows that three degree-of-freedom systems can yield a 250% improvement over two degree-of-freedom systems which themselves are practically able to provide three to four order of magnitude improvements in sensitivity over resonant-frequency based sensors of the same size. The tools and insight needed to design for higher degree-of-freedom system are also provided in the form of the eigen-derivatives approach to calculating eigenvalue and eigenvector sensitivity to disorder in a symmetric system.

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